%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN586-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:35:15 PM UTC 2026
% Result : Unsatisfiable 12.97s 2.11s
% Output : Proof 12.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 55 unt; 0 def)
% Number of atoms : 91 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 34 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 90 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,negated_conjecture,
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_17) ).
fof(f16_nnf,plain,
! [X9,X10,X11,X12] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X9,X10,X11,X12] :
( ~ p15(X11,X12)
| ~ p2(X12,X10)
| ~ p2(X11,X9)
| p15(X9,X10) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p15(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p15(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t29,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,ifeq(p15(X1,X3),true,p15(X2,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t42,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,ifeq(p15(X1,X3),true,p15(X2,X4),true),true),true) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(f21,negated_conjecture,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_22) ).
fof(f21_nnf,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(t20,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t83,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t84,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),X1),true,ifeq(p2(c20,X2),true,ifeq(true,true,p15(X1,X2),true),true),true),
inference(cp,[status(thm)],[t42,t83]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t33,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t6493,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),X1),true,ifeq(p2(c20,X2),true,p15(X1,X2),true),true),
inference(step,[status(thm)],[t84,t33]) ).
cnf(t5906,plain,
ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),X1),true,ifeq(p2(c20,X2),true,p15(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t6493]) ).
cnf(f22,negated_conjecture,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_23) ).
fof(f22_nnf,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t19,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20) = false,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t110,plain,
p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20) = false,
inference(orient,[status(thm)],[t19]) ).
cnf(t5910,plain,
true = ifeq(p2(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19))),true,ifeq(p2(c20,c20),true,false,true),true),
inference(cp,[status(thm)],[t5906,t110]) ).
cnf(f19,negated_conjecture,
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_20) ).
fof(f19_nnf,plain,
! [X16,X17,X18,X19] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X16,X17,X18,X19] :
( ~ p3(X17,X19)
| ~ p2(X16,X18)
| p2(f4(X16,X17),f4(X18,X19)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p2(f4(X0,X1),f4(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t26,plain,
ifeq(p2(X1,X2),true,ifeq(p3(X3,X4),true,p2(f4(X1,X3),f4(X2,X4)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t41,plain,
ifeq(p2(X1,X2),true,ifeq(p3(X3,X4),true,p2(f4(X1,X3),f4(X2,X4)),true),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f3,negated_conjecture,
p2(X13,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
! [X13] : p2(X13,X13),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X13] : p2(X13,X13),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t5,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t72,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t77,plain,
true = ifeq(true,true,ifeq(p3(X1,X2),true,p2(f4(X3,X1),f4(X3,X2)),true),true),
inference(cp,[status(thm)],[t41,t72]) ).
cnf(t6324,plain,
true = ifeq(p3(X1,X2),true,p2(f4(X3,X1),f4(X3,X2)),true),
inference(step,[status(thm)],[t77,t33]) ).
cnf(t3857,plain,
ifeq(p3(X1,X2),true,p2(f4(X3,X1),f4(X3,X2)),true) = true,
inference(orient,[status(thm)],[t6324]) ).
cnf(f11,negated_conjecture,
( ~ p3(X27,X28)
| p3(f11(X27),f11(X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_12) ).
fof(f11_nnf,plain,
! [X27,X28] :
( ~ p3(X27,X28)
| p3(f11(X27),f11(X28)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X27,X28] :
( ~ p3(X27,X28)
| p3(f11(X27),f11(X28)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p3(X0,X1)
| p3(f11(X0),f11(X1)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
ifeq(p3(X1,X2),true,p3(f11(X1),f11(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
ifeq(p3(X1,X2),true,p3(f11(X1),f11(X2)),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f4,negated_conjecture,
p3(c21,c19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).
fof(f4_nnf,plain,
p3(c21,c19),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p3(c21,c19),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t7,plain,
p3(c21,c19) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t62,plain,
p3(c21,c19) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t67,plain,
true = ifeq(true,true,p3(f11(c21),f11(c19)),true),
inference(cp,[status(thm)],[t39,t62]) ).
cnf(t5925,plain,
true = p3(f11(c21),f11(c19)),
inference(step,[status(thm)],[t67,t33]) ).
cnf(t134,plain,
p3(f11(c21),f11(c19)) = true,
inference(orient,[status(thm)],[t5925]) ).
cnf(t4095,plain,
true = ifeq(true,true,p2(f4(X1,f11(c21)),f4(X1,f11(c19))),true),
inference(cp,[status(thm)],[t3857,t134]) ).
cnf(t6330,plain,
true = p2(f4(X1,f11(c21)),f4(X1,f11(c19))),
inference(step,[status(thm)],[t4095,t33]) ).
cnf(t4164,plain,
p2(f4(X1,f11(c21)),f4(X1,f11(c19))) = true,
inference(orient,[status(thm)],[t6330]) ).
cnf(t6494,plain,
true = ifeq(true,true,ifeq(p2(c20,c20),true,false,true),true),
inference(step,[status(thm)],[t5910,t4164]) ).
cnf(t6495,plain,
true = ifeq(p2(c20,c20),true,false,true),
inference(step,[status(thm)],[t6494,t33]) ).
cnf(t6496,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t6495,t72]) ).
cnf(t6497,plain,
true = false,
inference(step,[status(thm)],[t6496,t33]) ).
cnf(t5912,plain,
false = true,
inference(orient,[status(thm)],[t6497]) ).
cnf(f5,negated_conjecture,
~ p12(f13(c20),f13(c18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_6) ).
fof(f5_nnf,plain,
~ p12(f13(c20),f13(c18)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ p12(f13(c20),f13(c18)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ p12(f13(c20),f13(c18)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c22]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5912]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN586-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 01:50:18 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.97/2.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.97/2.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------